bigstatsr and bigsnpr: two R packages for efficient analysis of SNP arrays.

# bigstatsr and bigsnpr: two R packages for efficient analysis of SNP arrays.
## BCM seminar – Vignette
### Florian Privé
### 2017/04/21

---

# Introduction

---

## Installation

Install packages [**bigstatsr**](https://github.com/privefl/bigstatsr) and [**bigsnpr**](https://github.com/privefl/bigsnpr)  from [Github](https://github.com/privefl):

```r
devtools::install_github("privefl/bigsnpr")
```

???

- Package bigsnpr is not finished yet.
- There still are some dependencies that are not on CRAN.

---

## Description

- bigstatsr: Statistics on `big.matrix` objects:

- Linear predictive models
  
  - SVD / PCA
  
  - Nice plotting functions
  
  - Parallelization / apply
  
  - Matrix operations

- bigsnpr: Special structure for SNP matrices and specific algorithms:

- wrapper for calls to external software (PLINK and Beagle)

- read (write) functions from (to) *bed*/*bim*/*fam* files
  
  - imputation

- pruning / clumping

???

- bigstatsr can be used for any field
- bigsnpr provides a special structure

---

## Object big.matrix

- Pointer to a matrix stored on disk1 with **simple** accessor
 - possibly much larger than your available RAM allowing computations on a laptop

- Many types: 
  - **`raw`**
  - `char`
  - `short`
  - **`integer`**
  - `float`
  - **`double`**
  
- A special `big.matrix` called **`BM.code`**
  
  stores 256 arbitrary different values

???

So matrices don't use RAM

---

## Data structure

Based on *bed*/*bim*/*fam*1 files:

- A `BM.code` corresponding to the *bed* file, the genotype matrix

- A `data.frame` containing SNP information (based on the *bim* file)

- A `data.frame` containing sample information (based on the *fam* file)

(2) Purcell S, Neale B, Todd-Brown K, Thomas L, Ferreira MAR, Bender D, Maller J, Sklar P, de Bakker PIW, Daly MJ & Sham PC (2007). PLINK: a toolset for whole-genome association and population-based linkage analysis. American Journal of Human Genetics, 81.
]

---

# First example analysis:

## Why pruning is important?

---

### A standard pipeline for association studies

- Quality control

- Imputation

- Statistical test

- Use of Principal Component Analysis (PCA) to correct for confounding with population structure1 (with pruning2)
 
- Plot results

.footnote[
[1] Price, Alkes L, Nick J Patterson, Robert M Plenge, Michael E Weinblatt, Nancy A Shadick, and David Reich. 2006. *Principal components analysis corrects for stratification in genome-wide association studies.* Nature Genetics 38 (8): 904–9.

[2] Price, Alkes L., Michael E. Weale, Nick Patterson, Simon R. Myers, Anna C. Need, Kevin V. Shianna, Dongliang Ge, et al. 2008. *Long-Range LD Can Confound Genome Scans in Admixed Populations.*
]

---

## Pre-analysis

### Quality control (and conversion) with PLINK

```r
library(bigsnpr)

plink <- "../../plink_linux_x86_64/plink"
prefix <- "../../POPRES_data/POPRES_allchr"

bedfileQC <- snp_plinkQC(plink.path = plink,
 prefix.in = prefix,
 file.type = "--file", # ped/map
 geno = 0.05,
 mind = 0.05,
 maf = 0.05,
 hwe = 1e-10,
 autosome.only = TRUE)

bedfileQC2 <- snp_plinkIBDQC(plink, bedfileQC, ncores = 11)
```

---

### Read bed/bim/fam in bigSNP format

```r
rdsfile <- snp_readBed(bedfileQC2, "popresQC")
popres <- snp_attach(rdsfile)
str(popres, max.level = 2, strict.width = "cut")
```

```
## List of 4
##  $ genotypes:Formal class 'BM.code.descriptor' [package "bigst"..
##  $ fam      :'data.frame':	1382 obs. of  6 variables:
##   ..$ family.ID  : chr [1:1382] "Croatia" "Serbia" "Czech" "Bo"..
##   ..$ sample.ID  : int [1:1382] 474 660 1890 1923 2083 2733 346..
##   ..$ paternal.ID: int [1:1382] 0 0 0 0 0 0 0 0 0 0 ...
##   ..$ maternal.ID: int [1:1382] 0 0 0 0 0 0 0 0 0 0 ...
##   ..$ sex        : int [1:1382] 2 1 1 1 1 1 2 1 1 2 ...
##   ..$ affection  : int [1:1382] -9 -9 -9 -9 -9 -9 -9 -9 -9 -9 ...
##  $ map      :'data.frame':	344614 obs. of  6 variables:
##   ..$ chromosome  : int [1:344614] 1 1 1 1 1 1 1 1 1 1 ...
##   ..$ marker.ID   : chr [1:344614] "SNP_A-1909444" "SNP_A-4303"..
##   ..$ genetic.dist: int [1:344614] 0 0 0 0 0 0 0 0 0 0 ...
##   ..$ physical.pos: int [1:344614] 742429 769185 775852 993492 ..
##   ..$ allele1     : chr [1:344614] "C" "G" "T" "G" ...
##   ..$ allele2     : chr [1:344614] "T" "A" "C" "A" ...
##  $ savedIn  : chr "backingfiles/popresQC.rds"
##  - attr(*, "class")= chr "bigSNP"
```

???

- backingfiles: ".rds" and ".bk"

---

### Some summaries (1/2)

```r
G <- popres$genotypes # 1382 x 344614 (would take 3.5 Gb)
```
--

```r
big_counts(G, ind.col = 1:10) 
```

```
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## 0 26 24 27 89 6 7 34 25 5 9
## 1 429 302 393 561 183 220 403 276 138 156
## 2 927 1056 962 732 1193 1155 945 1081 1239 1217
## <NA> 0 0 0 0 0 0 0 0 0 0
```
--

```r
big_counts(G, ind.row = 1:8, byrow = TRUE) 
```

```
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
## 0 28704 29045 29026 28557 29713 28808 28819 29252
## 1 120643 120072 119984 120646 119213 119825 120396 121079
## 2 195267 195497 195604 195411 195688 195981 195399 194283
## <NA> 0 0 0 0 0 0 0 0
```

---

### Some summaries (2/2)

```r
str(big_scale()(G))
```

```
## 'data.frame':	344614 obs. of  2 variables:
##  $ mean: num  1.65 1.75 1.68 1.47 1.86 ...
##  $ sd  : num  0.515 0.473 0.508 0.615 0.361 ...
```
--

```r
fNA <- function(x, ind) colSums(is.na(x[, ind]))

guess.it <- big_apply(G, a.FUN = fNA, a.combine = 'c')

rle(guess.it)  # 'Run Length Encoding'
```
--

```
## Run Length Encoding
##   lengths: int 344614
##   values : num 0
```

---

## SVD

```r
obj.svd <- big_randomSVD(G, fun.scaling = snp_scaleBinom(),
 k = 10, ncores = 11)
plot(obj.svd)
```

---

```r
(p <- plot(obj.svd, type = "scores"))
```

---

### Get population

```r
list.pops <- list(
 "SW Europe" = c("Portugal", "Spain"), 
 "Italy" = "Italy",
 "SE Europe" = c("Greece", "Turkey", "Cyprus", "Macedonia"),
 "Anglo-Irish Isles" = c("United", "Scotland", "Ireland"),
 "FennoScandia" = c("?orway", "Finland", "Sweden", "Denmark"),
 "Western Europe" = c("France", "Swiss-French", "Swiss-German", 
 "Swiss-Italian", "Belgium"),
 "Central Europe" = c("Germany", "Austria", "Poland", 
 "?etherlands"),
 "Eastern Europe" = c("Czech", "Romania", "Bulgaria", "Hungary", 
 "Albania", "Macedonia,", "Slovakia"),
 "Former Yugoslavia" = c("Croatia", "Serbia", "Bosnia",
 "Slovenia", "Kosovo"),
 "Former USSR" = c("Russian", "Ukraine", "Latvia")
)
mat.pops <- cbind(
 unlist(list.pops, use.names = FALSE),
 rep(names(list.pops), times = sapply(list.pops, length))
)
ind.match <- match(popres$fam$family.ID, mat.pops[, 1])
Population <- mat.pops[ind.match, 2]
```

---

```r
library(ggplot2)

p + aes(color = Population)
```

---

```r
plot(obj.svd, type = "loadings", loadings = 1:6,
     cols = 3, coeff = 0.6)
```

---

```r
oneSNP <- attach.BM(G)[, which.max(abs(obj.svd$v[, 3]))]

plot(obj.svd, type = "scores", scores = 3:4) +
  aes(color = as.factor(oneSNP)) +
  labs(color = "Genotype")
```

---

```r
plot(obj.svd, type = "scores", scores = 3:4) +
  aes(color = Population)
```

---

### Scores with pruning (clumping)

```r
# SVD with clumping
obj.svd2 <- snp_clumpedSVD(G, infos.chr = popres$map$chromosome, 
 ncores = 11)
```

---

```r
plot(obj.svd2, type = "scores", scores = 3:4) +
  aes(color = Population)
```

---

# Second example analysis:

## Polygenic risk scores of celiac disease

---

## Pre-analysis

### Quality control (and conversion) with PLINK

```r
library(bigsnpr)
library(ggplot2)

plink <- "../../plink_linux_x86_64/plink"
prefix <- "../Dubois2010_data/FinnuncorrNLITUK1UK3hap300"

bedfileQC <- snp_plinkQC(plink.path = plink,
 prefix.in = prefix,
 geno = 0.05,
 mind = 0.05,
 maf = 0.05,
 hwe = 1e-10,
 autosome.only = TRUE)

# ETC: 10 min
rel <- snp_plinkIBDQC(plink, bedfileQC, ncores = 11, 
 do.blind.QC = FALSE)
```

---

### Investigate relatedness

```r
MY_THEME <- bigstatsr:::MY_THEME

MY_THEME(qplot(y = PI_HAT, data = rel)) + 
  geom_hline(yintercept = 0.2) # visual inspection threshold
```

---

### Remove related individuals

```r
# remove 33 individuals
bedfileQC2 <- snp_plinkRmSamples(
 plink, 
 bedfile.in = bedfileQC, 
 bedfile.out = sub("\\.bed$", "_norel.bed", bedfileQC), 
 df.or.files = subset(rel, PI_HAT > 0.2)
)
```

### Read celiac data

```r
# Read the bed/bim/fam files once
snp_readBed(bedfileQC2, "celiacQC")
```
```
## [1] "backingfiles/celiacQC.rds"
```

```r
# Then, just attach the data
celiac <- snp_attach("backingfiles/celiacQC.rds")
G <- celiac$genotypes # 15250 x 281122 (would take 32 Gb)
```

---

### Missing values

```r
# Get some counts by SNP
counts <- big_counts(G)
counts[, 1:10]
```

```
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## 0 420 1174 427 1121 167 295 356 2057 81 605
## 1 4080 6086 4220 6009 2732 3570 3853 6880 2018 4640
## 2 10723 7982 10601 8119 12350 11383 11029 6300 13148 10000
## <NA> 27 8 2 1 1 2 12 13 3 5
```

```r
# Proportion of missing values
sum(counts[4, ]) / length(G)
```

```
## [1] 0.0004031312
```

---

### Imputation

#### Using Beagle

```r
# You can impute with Beagle (before reading)
beagle <- "../../../beagle.21Jan17.6cc.jar"
bedfileQC3 <- snp_beagleImpute(beagle.path = beagle,
 plink.path = plink,
 bedfile.in = bedfileQC2,
 memory.max = 30,
 ncores = 11)
```

Using `Beagle` to impute this dataset would take weeks!

#### Using XGBoost1

```r
infos <- snp_fastImpute(G, celiac$map$chromosome, ncores = 6)
```
took less than 6 hours to complete.

---

```r
plot(subset(infos, pNA > 0.001), pch = 19, cex = 0.5)
pvals <- c(0.01, 0.005, 0.002, 0.001); colvals <- 2:5
idc <- lapply(seq_along(pvals), function(i) {
 curve(pvals[i] / x, from = 0, lwd = 2, 
 col = colvals[i], add = TRUE)
})
legend("topright", legend = pvals, title = "p(NA & Error)",
 col = colvals, lty = 1, lwd = 2)
```

---

### After imputation

```r
big_counts(G, ind.col = 1:10)
```

#### Why are there still NAs?

```r
# underlying `big.matrix` (without `code`)
G2 <- attach.big.matrix(G)
typeof(G2)
```

```
## [1] "raw"
```

```r
head(G2[, 1], 10)
```

```
##  [1] 02 02 02 02 02 02 02 02 02 02
```

---

```r
table(as.integer(G2[, 1]))
```

```
## 
##     0     1     2     5     6 
##   420  4080 10723    19     8
```

```r
str(bigsnpr:::CODE_IMPUTE_PRED)
```

```
##  num [1:256] 0 1 2 NA 0 1 2 NA NA NA ...
```

```r
str(G, max.level = 2)
```

```
## Formal class 'BM.code.descriptor' [package "bigstatsr"] with 2 slots
##   ..@ code       : num [1:256] 0 1 2 NA NA NA NA NA NA NA ...
##   ..@ description:List of 13
```

```r
*G@code <- bigsnpr:::CODE_IMPUTE_PRED
big_counts(G, ind.col = 1:10)
```

```
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## 0 420 1174 428 1121 167 295 356 2057 81 605
## 1 4099 6091 4221 6010 2732 3570 3863 6886 2019 4642
## 2 10731 7985 10601 8119 12351 11385 11031 6307 13150 10003
## <NA> 0 0 0 0 0 0 0 0 0 0
```

---

#### SVD with clumping

```r
obj.svd <- snp_clumpedSVD(G, celiac$map$chromosome, ncores = 11)
```

#### Get information on population

```r
# Get population from external files
pop.files <- list.files(path = "../Dubois2010_data/", 
 pattern = "cluster_*",
 full.names = TRUE)
# data.table::fread(pop.files[1])
readLines(pop.files[1], n = 3)
```

```
## [1] "1\t131458\t5" "1\t131945\t5" "1\t191795\t5"
```

```r
pop <- snp_getSampleInfos(celiac, pop.files)[[1]]
pop.names <- c("Netherlands", "Italy", "UK1", "UK2", "Finland")
rle(pop.names[pop])
```

```
## Run Length Encoding
##   lengths: int [1:5] 6766 3331 2474 1640 1039
##   values : chr [1:5] "UK2" "UK1" "Finland" "Netherlands" ...
```

---

```r
(p <- plot(obj.svd, type = "scores", scores = 1:2) +
 aes(color = pop.names[pop]) +
 labs(color = "Population"))
```

---

### Interactive plot

```r
plotly::ggplotly(p + aes(text = asPlotlyText(celiac$fam)),
                 tooltip = "text")
```

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---

## GWAS

```r
# ETC: 5 min
y01 <- celiac$fam$affection - 1

gwas <- big_univLogReg(G, y01.train = y01, 
 covar.train = obj.svd$u, 
 ncores2 = 6)
```

---

```r
snp_qq(gwas) + xlim(1, NA)
```

```
## Warning: Removed 253010 rows containing missing values
## (geom_point).
```

---

```r
labels <- 1:22; labels[c(4, 6, 8, 10, 12, 14, 16:17, 19:21)] <- ""
(p <- snp_manhattan(snp_gc(gwas), 
 infos.chr = celiac$map$chromosome,
 infos.pos = celiac$map$physical.pos, 
 labels = labels,
 npoints = 5e3))
```

---

### Interactive Manhattan plot

```r
ind <- attr(p, "subset")
plotly::ggplotly(p + aes(text = asPlotlyText(celiac$map[ind, ])),
 tooltip = "text")
```

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---

## Statistical predictions

```r
ind.train <- sort(sample(nrow(G), 10e3))
ind.test <- setdiff(rows_along(G), ind.train) # 5250

gwas.train <- big_univLogReg(G, y01.train = y01[ind.train],
 ind.train = ind.train,
 covar.train = obj.svd$u[ind.train, ],
 ncores2 = 6)
```

---

### Polygenic Risk Score (PRS)

#### Clumping

```r
ind.keep <- snp_clumping(G, infos.chr = celiac$map$chromosome,
 ind.row = ind.train,
 S = abs(gwas.train$score),
 size = 500, # the default
 thr.r2 = 0.5 # the default
 ncores = 11)
```

#### Different values of thresholding

```r
thrs <- seq(0, 400, 5)
lpS <- -predict(gwas.train)
nb.pred <- sapply(thrs, function(thr) sum(lpS[ind.keep] > thr))

prs <- snp_PRS(G, betas = gwas.train$estim,
 ind.test = ind.test,
 ind.keep = ind.keep,
 lpS = lpS, 
 thr.list = thrs)

aucs <- apply(prs, 2, AUC, target = y01[ind.test])
```

---

### AUC ~ #predictors

```r
MY_THEME(qplot(nb.pred, aucs)) + scale_x_log10()
```

---

### Logistic regression

```r
# logistic regression with elastic-net regulization
logistic <- big_spLogReg(G, y01.train = y01[ind.train],
 ind.train = ind.train,
 covar.train = obj.svd$u[ind.train, ],
 alpha = 0.5, 
 dfmax = 20e3)
```

```r
pred.logistic <- predict(logistic, G, ind.row = ind.test, 
 covar.row = obj.svd$u[ind.test, ])

aucs2 <- apply(pred.logistic, 2, AUC, target = y01[ind.test])
```

```r
library(Matrix)
nb.pred2 <- colSums(logistic$beta != 0)
```

---

### AUC ~ #predictors

```r
MY_THEME(qplot(nb.pred2, aucs2)) 
```

---

## In perspective

- Comparison of PCA with or without pruning in different applications

- Comparison of different statistical models of prediction in different cases of genetic architecture of disease.

- Comparison of imputation with XGBoost and other methods

---

# Thanks!

## Any questions?